刚体运动三维可视化模拟和复摆相关问题探讨

Three-dimensional simulation and visualization of the motion of rigid body and discussion on physical pendulum related problems

本文应用刚体定轴转动定律和角动量定理,结合VPython软件,首先模拟刚体的定轴转动,例如匀质圆柱体在不同力矩作用下的转动,直观地显示刚体运动轨迹以及角位移、角速度等物理量随时间的变化关系,以及重力矩作用下的刚体能量守恒等,使刚体运动过程实现可视化.有趣的是,本文还研究了刚体的平面平行运动(平动加转动)以及刚体的振动,模拟了大角度下刚体摆动时出现的混沌状态.可视化模拟深化了对课本知识的理解.

In this paper,the rotational motion of rigid body around a fixed axis is studied by using Newton’s second law for rotation and in angular form with VPython software.Some special examples discussed in detail are motions of rotating uniformly rod under different torques,the path,angular displacement,angular velocity and moving process,and were visualized intuitively in real time.The conservation of the energy of rotating rigid rod only experienced with torque of gravity can be verified by VPython software.The plane motion of rigid body(translation plus rotation)and vibration of rigid body are also studied.Especially,the chaos state of rigid rod with large rotating angle is investigated.The simulation deepens the understanding of textbook knowledge.